Single kinesin molecules (a motor protein) have been shown to be able to move unidirectionally on a microtubule (a periodic biopolymer made of identical monomer subunits) by catalyzing the hydrolysis of ATP. Exactly how the chemical free energy of ATP hydrolysis is converted into mechanical energy in this system is not clear. In the last report, we showed that an enzymatic Brownian particle can be driven to move unidirectionally on a static periodic electric potential field by the free energy of the chemical reaction it catalyzes, if at least one of the intermediates of the catalytic cycle is charged and the potential field in each period is not symmetrical. This is the first model with explicit mechanisms showing how chemical-mechanical free energy transduction is carried out. This year, we have extended the research further and concentrated our work on two problems. First, we examined how the Brownian particle behave when the enzymatic reactions of the particle contains more than one cycle and more than one charged states. It was found that the direction of the particle movement depended not only on the asymmetry of the potential, but also on the detailed mechanisms of the catalytic reactions. This result suggests an experimental separation method for protein molecules based on their enzymatic activities. Second, the formalism and the calculation procedure have been extended and reformulated so that they become applicable to kinesin molecules. In general, the existence of a static periodic electric field near the surface of a microtubule is not very likely. Therefore, the model based on direct interaction between charged states and a periodic asymmetric electric field may not be directly applicable to the kinesin system. Instead, we have used the same "cross-bridge" concept as in muscle contraction, where force is generated by attaching a part of the kinesin (the cross- bridge) to a specific binding site on each monomer of the microtubule. The formalism is currently used in assessing the mechanisms of kinesin movement based on in vitro experimental data.